It's a gradual process - as American wares flowed to Europe post WW1 so did American movies, music, food and general culture - same will happen with China.. Your culture does not become the dominant the instant your economy is the biggest. In Europe we are just used to exporting culture at gun point because that's what we did for the last 500 years.
So did America at first - in fact they were pretty dead set on staying isolated and minding their own business, both figurative and literally.